<html>

<head>
<meta http-equiv="Content-Language" content="en-us">
<meta name="GENERATOR" content="Microsoft FrontPage 5.0">
<meta name="ProgId" content="FrontPage.Editor.Document">
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
<title>Purpose of Maps</title>
</head>

<body>

<p><font color="#0000FF"><b>Beam physics</b></font> can be divided into two groups: ray tracing group and Taylor 
series group.</p>
<p>1)<font color="#FF0000"> </font>In <font color="#FF0000"><b>single pass 
systems</b></font> such as spectrometers and electron microscopes, the 
computational effort is centered on the computation of the Taylor series 
expansion around a particular orbit, usual the so-called design orbit or optical 
axis.</p>
<p>2) In <b><font color="#FF0000">multi-pass systems </font></b>such as rings, 
one tries to study the stability of the system and excursion away from the 
so-called design orbit are of interest. For that reason, the validity of a 
Taylor map is more dubious. It is more appropriate in our view to integrate the 
trajectory in the old fashion way.</p>
<p>However, even in case 2, the properties around a particular orbit are of 
interest. In accelerators one may want to know the lattice functions, the 
chromaticities or even some low order nonlinear distortions in an attempt to 
understand the motion and to quantify it.</p>
<p>FPP provides automatic tools to extract a map from an integrator and analyze 
it. The most common analysis tool is the normal form. </p>

<p><font color="#0000FF"><b>Non beam physics</b></font> applications</p>
<p>3) General maps: sometimes we must deal with general vectorial equations. For 
that purpose FPP has a type GMAP. </p>
<p>&nbsp;</p>

</body>

</html>